Gear Module Calculator

Calculate gear module (metric) or diametral pitch (Imperial) from pitch diameter and number of teeth.

Calculator

mm
teeth

Example Result

Your result will appear here

The calculated result will appear here after you press Calculate.

About the Gear Module Calculator

Gear module is the fundamental size parameter for metric gears. It defines the size of each tooth relative to the gear diameter, and it determines which gears can mesh together — only gears with the same module can be paired. The module formula m = d / N divides the pitch circle diameter by the number of teeth. Module is always expressed in millimetres. Standard module values follow the ISO 54 series: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50. In Imperial engineering, the equivalent parameter is diametral pitch (DP = N / d, in teeth per inch), where larger DP values indicate finer, smaller teeth. This calculator converts between both systems automatically so you can work in whichever standard your application requires and verify compatibility with existing components.

How to Use the Gear Module Calculator

  1. 1

    Select SI (metric, mm) or Imperial (inches) to match your drawing or component.

  2. 2

    Enter the pitch circle diameter — this is the theoretical diameter at which gears mesh, shown on most gear drawings.

  3. 3

    Enter the number of teeth on the gear.

  4. 4

    Press Calculate. Module (or diametral pitch) is shown along with the nearest standard value for gear procurement.

Gear Module Calculator Examples

Frequently Asked Questions

What is gear module?

Gear module (m) is the ratio of the pitch circle diameter to the number of teeth: m = d / N. It standardises tooth size for metric gears — a higher module means larger, stronger teeth. Gears can only mesh if they have the same module.

What are standard gear module values?

ISO 54 defines the preferred metric module series: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25, 32, 40, 50 mm. When designing a gear, always round your calculated module up to the nearest standard value for off-the-shelf availability.

What is diametral pitch and how does it relate to module?

Diametral pitch (DP) is the Imperial equivalent of module. It is the number of teeth per inch of pitch diameter: DP = N / d. The relationship between module and diametral pitch is m = 25.4 / DP. A higher DP means smaller, finer teeth.

Can I mesh a metric gear with an Imperial gear?

Only if their tooth geometry is compatible. Metric and Imperial gears use the same 20-degree pressure angle in most modern designs, but the tooth size will only match if the module (metric) equals 25.4 divided by the diametral pitch (Imperial) to within manufacturing tolerances. In practice, this is rarely the case, and mixing standards is not recommended.

What is the relationship between module and tooth size?

Module directly determines tooth height and pitch. Addendum (tooth height above pitch circle) equals 1 × m. Dedendum (tooth depth below pitch circle) equals 1.25 × m. Tooth pitch (distance between adjacent teeth along the pitch circle) equals π × m. A module 2 gear has a tooth pitch of 6.28 mm.

How do I choose the right module for my gear?

Module is chosen based on the load capacity required. A rough guide: module 1–2 for light instrument gears, module 2–4 for medium industrial gears, module 5–10 for heavy machinery. The exact module is determined by gear strength calculations based on transmitted torque, contact stress, and material properties.

What is the pitch circle diameter?

The pitch circle diameter (PCD) is the theoretical circle on which gear teeth are considered to mesh. Two meshing gears appear to roll against each other along their pitch circles. The centre distance between two meshing gears equals the sum of their pitch radii: C = (d1 + d2) / 2.

How do I calculate the centre distance between two gears?

Centre distance C = (d1 + d2) / 2 = m × (N1 + N2) / 2, where m is the common module and N1, N2 are the tooth counts of the two gears. For example, a module 3 gear with 20 teeth meshing with a module 3 gear with 40 teeth: C = 3 × (20 + 40) / 2 = 90 mm.

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How Module and Diametral Pitch Are Calculated

Two gears mesh only if their teeth are the same size. Metric gears give tooth size as the module m = d / N (pitch-circle diameter per tooth, in millimetres); inch gears use diametral pitch DP = N / d (teeth per inch of pitch diameter). The two are linked by DP = 25.4 / m.

From the module follow the other basic dimensions of a standard full-depth tooth: addendum a = m, outside diameter d + 2m = m(N + 2), and the centre distance of a pair a = m(N₁ + N₂)/2. The calculator also shows the nearest preferred module (ISO 54 first-choice series: 1, 1.25, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25 mm) or the nearest standard DP.

SymbolMeaning
mModule, mm (metric tooth size)
DPDiametral pitch, teeth per inch (inch tooth size)
dPitch (reference) circle diameter
NNumber of teeth
aAddendum = m (or 1/DP) for a standard full-depth tooth

Gear Sizes From Module and Teeth

  1. 1SI: 48 teeth on a 96 mm pitch diameter.

    m = 96 / 48; DP = 25.4 / m; outside diameter = 96 + 2 × m

    Module = 2 mm (standard) · DP = 12.7 · Addendum = 2 mm · Outside diameter = 100 mm

    A standard module 2 gear; 100 mm is the size you would measure across the tips with a caliper.

  2. 2Imperial: an unknown 25-tooth gear measures 2.25 in across the tips. Pitch diameter for a full-depth tooth: d = OD × N / (N + 2) = 2.25 × 25 / 27 = 2.0833 in.

    DP = 25 / 2.0833; m = 25.4 / DP

    DP = 12.0 → standard DP 12 · Module equivalent = 2.117 mm

    A DP 12 gear. It is not interchangeable with module 2 (2.117 mm vs 2.000 mm, about 6% larger teeth) — the pair would bind.

Reading the Gear Dimensions

A result close to a standard module or DP confirms the measurement; a value between standard sizes usually means a measurement error, a worn gear, or an inch gear measured in millimetres (or the reverse).

Matching module is necessary but not sufficient: the pressure angle must match too (20° is standard; older inch gears may be 14.5°), and helical gears must also match helix angle and hand.

What These Gear Formulas Assume

  • Spur gears, standard toothAddendum = 1 × module (ISO 53 basic rack). Stub or modified teeth have different outside diameters.
  • Pitch diameter inputEnter the pitch (reference) diameter, not the outside diameter; convert with d = OD × N / (N + 2).
  • Helical gearsUse the transverse module for diameters and the normal module for the cutter.

Gear Sizing Slips

  • Using the outside diameterMeasuring across the tips and entering it as the pitch diameter gives a module that is too large by (N + 2)/N.
  • Mixing systemsModule 2 (DP 12.7) and DP 12 look alike but do not mesh.
  • Ignoring pressure angleSame module with 14.5° and 20° pressure angles will not run together properly.

Sources

  1. ISO 54:1996 — Cylindrical gears for general engineering and for heavy engineering — Modules
  2. ISO 53:1998 — Cylindrical gears — Standard basic rack tooth profile — addendum = 1 × module
  3. KHK Gears catalogue, SH3-20L — module 3, 20 teeth → reference diameter 60 mm

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